Slope Intercept Form Quiz

In the year 3000, two robots, Benjamin and Nora, are positioned at two different coordinates on a digital grid in a virtual park. Benjamin is at coordinate (2, 3) and Nora is at coordinate (5, 9). If a digital line is drawn connecting these two coordinates, what is the slope of that line?

• 2

• 5

• 10

• 3

In the year 3000, Abigail is assisting Zoe in programming an AI to understand the concept of slope-intercept form in a mathematical algorithm. She explains that if a line in a 2D graph representing the AI's learning curve has a slope of 4 and a y-intercept of 2, what would be the equation of the line in slope-intercept form?

• y = 4x + 2

• y = 4x - 2

• y = 2x + 4

• y = 2x - 4

In the year 3000, three androids named Jackson, Ava, and Anika are analyzing the energy output of a futuristic power grid. The energy output is represented by a graph with the equation y = 3x - 5. They need to identify the rate of energy output (slope) and the base energy level (y-intercept) from this graph. What are the correct values?

• Rate of energy output = -3, Base energy level = 5

• Rate of energy output = 5, Base energy level = 3

• Rate of energy output = 0, Base energy level = 3

• Rate of energy output = 3, Base energy level = -5

In the future, Michael is helping Mia to understand how to graph linear equations in a virtual reality environment. He decided to use a real-world example. He asked Mia to imagine a scenario where the number of energy units (y) she has depends on the number of solar panels (x) she installs. The relationship is given by the equation y = 2x + 1. Can you help Mia to graph this equation in the virtual reality environment?

• Graph the equation y = 2x - 1 by imagining that for each solar panel Mia installs, she gets 2 energy units, but she starts with -1 energy unit. Plot the y-intercept at (0, -1) and use the slope of 2 to find another point on the line.

• Graph the equation y = 2x + 1 by imagining that for each solar panel Mia installs, she gets 2 energy units, but she starts with 1 energy unit. Plot the x-intercept at (1, 0) and use the slope of 2 to find another point on the line.

• Graph the equation y = 2x + 1 by imagining that for each solar panel Mia installs, she gets 3 energy units, but she starts with 1 energy unit. Plot the y-intercept at (0, 1) and use the slope of 3 to find another point on the line.

• Graph the equation y = 2x + 1 by imagining that for each solar panel Mia installs, she gets 2 energy units, but she starts with 1 energy unit. Plot the y-intercept at (0, 1) and use the slope of 2 to find another point on the line.

In the year 3000, Nora is operating a hovercraft charging station on Mars. She charges each hovercraft for $2. If she charges 4 hovercrafts, and has to pay Anika $3 for assisting her, how much money will Nora have?

• Nora will have 2(4) - 3 = 8 - 3 = $5

• Nora will have 2(4) - 3 = 8 + 3 = $11

• Nora will have 2(4) - 3 = 4 - 3 = $1

• Nora will have 2(4) - 3 = 8 * 3 = $24

In the year 3000, two robots, ElijahBot and HannahBot, are positioned at different coordinates on a space station. ElijahBot is at point (-1, 4) and HannahBot is at point (3, 10). If they establish a direct communication line between them, what would be the slope of that line?

• m = (10 - 4) / (3 - (-1)) = 6 / 2 = 3

• m = (10 - 4) / (3 - (-1)) = 6 / 4 = 1.5

• m = (10 - 4) / (3 - (-1)) = 6 / 3 = 2

• m = (10 - 4) / (3 - (-1)) = 6 / 5 = 1.2

In the year 3000, three scientists, Lily, Abigail, and Priya are working on a project to design a hyperloop track on Mars. They need to calculate the equation of a track segment that represents a hill's slope. The hill has a slope of -3, and it starts 7 meters above the Martian surface. They need to write this in slope-intercept form. What equation should they write?

• y = -7x + 3

• y = -3x + 7

• y = 3x + 7

• y = -3x - 7

In the year 3000, a robot named Zeta is teaching an AI named Alpha about the concept of slope and y-intercept in the context of plotting a course for a spaceship. Zeta uses the equation y = -2x + 4 as an example. Can Alpha identify the slope and y-intercept from this equation?

• Slope = 2, Y-intercept = -4

• Slope = -2, Y-intercept = 4

• Slope = 0, Y-intercept = 4

• Slope = -4, Y-intercept = 2

Nora, Scarlett, and Elijah are astronauts trying to navigate their way to a hidden treasure on a distant planet. The map they have says 'Start at the spaceship (which they decided is the origin) and move along the path defined by the equation y = -x + 3.' How should they interpret this in the zero-gravity environment?

• Option A: They should start at the spaceship and move in a direction such that for every step they float to the right, they float one step down, until they are 3 steps away from the spaceship.

• Option C: They should start at the spaceship and move in a direction such that for every step they float to the right, they float three steps down.

• Option B: They should start at the spaceship and move in a direction such that for every step they float to the right, they float one step up, until they are 3 steps below the spaceship.

• Option A: They should start at the spaceship and move in a direction such that for every step they float to the right, they float one step up, until they are 3 steps away from the spaceship.

In the year 3000, Samuel is operating a hovercraft charging station. He charges each hovercraft for $3 and has a fixed cost of $2 for the station's operation. If Elijah charges 5 hovercrafts, how much total money does Samuel make?

• Samuel makes 3(5) - 2 = 15 + 2 = 17 dollars

• Samuel makes 3(5) - 2 = 5 - 2 = 3 dollars

• Samuel makes 3(5) - 2 = 15 - 2 = 13 dollars

• Samuel makes 3(5) - 2 = 3 - 2 = 1 dollar